Related papers: On the counting function for numerical monoids

These notes present an approach to obtaining monoid operations which are compatible with a given family of mappings in the sense that the mappings become left translations in the monoid. This can be applied to various situations such as the…

We estimate the lattice sums arising in the context of the integer point counting in polyhedra.

The article presents a complete classification of $n$-valued monoids and groups of order 3. Important corollaries of this result are discussed.

We give a generating function for the number of unimodal permutations with a given cycle structure.

In this paper, we will give some estimation for the average error of the prime number theorem.

We give a number of theoretical and practical methods related to the computation of L-functions, both in the local case (counting points on varieties over finite fields, involving in particular a detailed study of Gauss and Jacobi sums),…

We seek to understand the physical significance of the nucleon's tensor charge and make estimates of its size in phenomenological models and the QCD sum rule.

We establish a central limit theorem for the eigenvalue counting function of a matrix of real Gaussian random variables.

We outline a method of calculation of partition functions of orientable manifolds with fluctuating metric and perform the calculation for the specific case of the unit interval.

In this article, firstly, some simple and smoothness properties of the weighted numerical radius and the weighted Crawford number functions are investigated. Then, some generalization formulas for lower and upper bounds of the weighted…

We find a nontrivial upper bound on the average value of the function M(n) which associates to every positive integer n the minimal Hamming weight of a multiple of n. Some new results about the equation M(n)=M(n') are given.

Calculating the values of nuclear correlation functions is computationally intensive due to the fact that the number of terms in a nuclear wave function scales exponentially with atomic number. To speed up this computation, we represent a…

In this article, we give a formula for the generalization of the binomial coefficient to the complex numbers as a linear combination of $\sinc$ functions. We then give a general formula to compute the integral on the real line of the…

We present a number of complexity results concerning the problem of counting vertices of an integral polytope defined by a system of linear inequalities. The focus is on polytopes with small integer vertices, particularly 0/1 polytopes and…

In this manuscript, we investigate some properties of certain counting functions, associated to the ergodic sums computed along the periodic orbits of the skew-product map, related to a finitely generated rational semigroup. To be precise,…

We study sums of arithmetic functions, defined on Gaussian integers and taken over those pairs of integers whose coordinates give rise to a singular system.

We survey the classical results on the prime number theorem

For any finite field $\mathbb{F}$ and any positive integer $n$ we count the number of monic polynomials of degree $n$ over $\mathbb{F}$ with nonzero constant coefficient and a self-reciprocal factor of any specified degree. An application…

We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first $N$ terms of the series. We show several examples of its application in calculating…

The main purpose of this paper is to construct not only generating functions of the new approach Genocchi type numbers and polynomials but also interpolation function of these numbers and polynomials which are related to a, b, c arbitrary…